Low-Relaxation Strand Practical Applications in Precast Prestressed Concrete

Transcription

1 Low-Relxtion Strnd Prcticl Applictions in Precst Prestressed Concrete Leslie D. Mrtin Consulting Engineer The Consulting Engineers Group, Inc. Glenview, Illinois Donld L. Pellow Supervisor Technicl Services Armco Inc., Union Wire Rope Knss City, Missouri The development of seven-wire stress-relieved strnd ws one of the most importnt fctors in the growth of prestressed concrete s stndrd mteril of construction. Just s the precst, prestressed concrete industry hs mtured into using wider, deeper, hevier nd more economicl sections, so the seven-wire strnd hs lso chnged to meet this demnd. From bsic stndrd of 25 ksi (172 MP) in 3/s, /is, nd r/z in. (1, 11, nd 13 mm) dimeter 25 yers go, strnd hs developed to the point where.5 nd.6 in. (13 nd 15 mm), 27 ksi (186 MP) is the stndrd used tody. In ddition, low-relxtion strnd is now mking its presence felt over the once commonly used stress-relieved mteril becuse it hs significntly less loss of initil tension. This cn result in improved nd more predictble service performnce, nd in mny cses will llow higher lod crrying cpbility. In 1957, the Americn Society for Testing nd Mterils issued the first "Stndrd Specifictions for Uncoted Seven-Wire Stress-Relieved Strnd for Prestressed Concrete" (ASTM A416). Tody, the 198 ASTM A416 stndrd' includes low-relxtion strnd. This specifiction requires tht the low-relxtion strnd differ from ordinry stress-relieved strnd in only two respects: first, it must meet certin relxtion loss requirements, s mesured by ASTM E3282 (note tht ordinry stress-relieved strnd hs no such requirement); nd second, the minimum yield strength, s mesured by the 1 percent extension under lod method, 84

2 must be not less thn 9 percent of the specified minimum breking strength, s opposed to 85 percent for norml stress-relieved strnd. All other requirements re the sme. This pper presents the results of n nlyticl study of the use of low-relxtion strnd in the most commonly used precst prestressed products. Most of the dt were obtined from the computer progrm LODTAB, which ws the progrm used to generte the design lod tbles in the PCI Design Hndbook3 nd those used by severl precst concrete producers in their own ctlogs. This progrm permits prestress losses to be input s fixed percentge of initil tension, or clculted by the method recommended by Zi et l.4 In ddition to compring lod cpbility nd service performnce, some concerns expressed by potentil users nd specifiers will be ddressed. [t should be noted tht this study only compres the mximum cpbility of the members, bsed on the bove method of loss clcultion. The strnd svings shown re for those conditions. Overll strnd svings to the precster or on project will be function of the product mix nd the number of members designed to pproch mximum cpcity. Loss of Prestress Until the mid-196's, the most common design prctice ws to ssume lump sum vlue of 35, psi (241 MP) for prestress loss for pretensioned members. This vlue is bsed on the 1958 report of ACI-ASCE Committee 323, 5 which served s the bsis for design for prestressed concrete until the first ACI Code provisions in This vlue is still mentioned in the ACI Code Commentry s giving "stisfctory results for mny pplictions." However, the performnce of some long-spn, hevily prestressed members seemed to indicte tht the lump Synopsis This pper evlutes the dvntges of designing prestressed concrete members with low-relxtion strnd. It lso investigtes the fesibility of using higher initil strnd tension (75 percent of nominl breking strength), nd nswers some of the questions regrding the most efficient use of low-relxtion strnd nd wht effects mixing it with stress-relieved strnd might hve. The min conclusions of this pper show tht low-relxtion strnd cn result in strnd svings, especilly in the longer, hevier structurl members. Low-relxtion strnd cn lso provide improvements in deflection nd crcking control. It is lso shown tht low-relxtion strnd cn be mixed with stress-relieved strnd in design bsed on stress-relieved strnd properties without hrmful effects. sum vlue underestimted the totl loss. In 1971, the PCI Design Hndbook Committee selected uniform vlue of 22 percent of initil (jcking) tension for use in the lod tbles in the first edition of the Hndbook, which ws lso retined in the second edition. For 27-ksi (186 MP) strnd stressed to 7 percent of ultimte, tht vlue is 41,58 psi (287 MP). The ACT Building Code s specifies the fctors which contribute to prestress loss for pretensioned members. They include the long-term effects of creep, shrinkge nd tendon relxtion, nd the immedite (upon relese) effect of elstic shortening. Considerble reserch hs been done on the subject, resulting in vriety of design recommendtions. Reference 4 includes PCI JOURNAUJuly-August

3 bibliogrphy of these reserch recommendtions. In 1975, the PCI Committee on Prestress Losses presented report which included generl nd simplified method for computing losses. As with mny of the other methods mentioned bove for mny members, this method seemed to predict vlues tht were higher thn experience could justify. In 1979, working group of ACI- ASCE Committee 423, Prestressed Concrete, developed clcultion method which ws lrgely bsed on erlier work, tempered by the experience of members of the group.' This clcultion method is the one used in this study. One of the primry differences between this method nd others is tht upper limits re included. However, no lower limits re specified, nd subsequent use of these equtions sometimes yields vlues which re suspiciously low. Therefore, the progrm LODTAB lso plces lower limit of 35, psi (241 MP) for stress-relieved strnd, nd 3, psi (27 MP) for low-relxtion strnd. It should be noted tht prestress loss hs virtully no effect on the ultimte strength of the member, t the level of prestress normlly used in pretensioned products. Initil (Jcking) Tendon Stress It hs been the prctice in the precst, prestressed concrete industry to pply n initil tension of 7 percent of the nominl strength of the strnd when using ordinry stress-relieved strnd. Stress relxtion losses in ordinry strnd hve been shown to be proportionlly higher when n initil stress higher thn 7 percent is used, to the point tht the gin in ctul prestressing of the concrete is miniml. With low-relxtion strnd, the relxtion loss remins more or less proportionl up to n initil stress of 75 percent of ultimte, so there is often definite dvntge of higher tensioning forces. Furthermore, ll mnufcturers of low-relxtion strnd pprove the use of the higher stressing force t 75 percent of nominl strength. Comprison of Lod-Crrying Cpbility The flexurl cpcity of prestressed concrete members is limited by two criteri: (1) Stresses t service lod nd (2) Ultimte design strength. In ddition, the ACI Building Code nd the AASHTO specifictions limit the concrete stress t the time of trnsfer of prestress. When the ultimte design strength of members is clculted using comptibility of strins, there is some indiction tht low-relxtion strnd my provide somewht greter cpcity thn ordinry stress-relieved strnd becuse the minimum yield strength is higher. However, typicl stress-strin curves shown in the PCI Design Hndbook mke no distinction between the two mterils. The curves in the Hndbook were checked ginst bout 25 ctul curves of both types from different mnufcturers, nd little difference ws found. The computer progrm LOD- TAB is bsed on these typicl stressstrin curves, so no difference in ultimte design strength will be indicted. The ctul re of both stress-relieved nd low-relxtion strnd my be somewht different from the re shown in ASTM A416. However, the stndrd specificlly exempts crosssectionl re from ny tolernce limittion. The minimum breking strength is specified s specific force, which is the product of the strnd grde [25 or 27 ksi (172 or 186 MP)] times the nominl or specified strnd re. For exmple, while the ctul crosssectionl re of 1/2 in. (13 mm) 27 ksi (186 MP) strnd is, sy,.158 sq in. (12 mm 2 ), the minimum breking 86

4 strength is 41.3 kips (27 x.153) (285 MP). Therefore, the nominl re of the strnd [e.g.,.153 sq in. (99 mm2) for '/2 in. (13 mm) dimeter] should lwys be used for design nd for the initil force to be pplied to the strnd. The ACI Building Code permits mximum tensile stress under service lod of 12 J (1. ) provided certin deflection criteri re met. It is common prctice in the prestressed concrete industry to design to this mximum in stemmed deck members such s double tees nd single tees. For flt deck members, such s hollow-core slbs, nd for bems, the most common prctice is to limit the tensile stress to 6,[f, (.5 J). This is the procedure followed in the PCI Design Hndbook nd in the nlyses tht follow. In ddition to flexurl criteri, it is common prctice to lso limit loding in hollow-core nd solid-slb deck members to the sher strength of the concrete, since it is very difficult to reinforce for sher. Since the mount of prestress in slb influences the sher strength, slbs which use low-relxtion strnd my hve slightly higher cpcity t hevily loded short spns. This effect is minor, however. A vriety of precst, prestressed concrete sections commonly used in building nd bridge construction were investigted in this study, s listed below. The building sections nd strnd ptterns were tken from the second edition of the PCI Design Hndbook.' The number in prentheses refers to the pge from tht publiction on which the section ppers. (Note: for the hollow-core section investigted, ctul strnd numbers nd sizes were used rther thn the "strnd designtion code" used in the Hndbook.) (1) 8 in. Hollow-core, norml weight-4hc8 (p. 2-27) Strnd ptterns: 7%, 4½, 51/2, 6 1/2, 7½ in. Stright strnds t 1'/2 in. from bottom (2) 12-in. Hollow-core, norml weight-4hc12 (p. 2-31) Strnd ptterns: 6½, 7Y2, 8½ in. Stright strnds t 1½ in. from bottom (3) 12-in. Hollow-core, norml weight, with 2 in. norml weight composite topping- 4HC (p. 2-31) Strnd ptterns: 6V2, 7½, 8½ in. Stright strnds t 1½ in. from bottom (4) 24-in. Double tee, norml weight-8dt24 (p. 2-16) Strnd ptterns: 68-S, 18-D1, 128-D1, 148-D1 (5) 24-in. Double tee, norml weight, with 2 in. norml weight composite topping- 8DT (p. 2-16) Strnd ptterns: 68S-18-D1, 128-Di (6) 24-in. Double tee, lightweight concrete-8ldt24 (p. 2-17) Strnd ptterns: 68-S, 18-D1, 128-D1, 148-D1 (7) 32-in. Double tee, norml weight-8dt32 (p. 2-18) Strnd ptterns: 168-D1, 188-D1, 28-D1, 228-D1 (8) 36-in. Single tee, norml weight-8st36 (p. 2-22) Strnd ptterns: 168-D1, 188-DA, 28-D1, 228-D1 (9) 36-in. Single tee, lightweight-8lst36 (p. 2-23) Strnd ptterns: 168-D1, 188-D1, 28-D1, 228-D1 (1) Inverted tee bem 241T36 (p. 2-52) Strnd ptterns: 12, 14, 16, 18, nd 2 stright strnds (11) Type IV AASHTO girders with 24, 3, 33, 36, nd 42 strnds. For ech of the sections nd strnd ptterns, three seprte lod tbles were generted: one with ordinry 27 ksi (186 MP) stress-relieved strnd, Note: 1 in. = 25.4 mm. PCI JOURNALJJuIy-August

5 initilly tensioned to.7 of the gurnteed ultimte strnd strength fp ); one with 27 ksi (186 MP) low-relxtion strnd initilly tensioned to.7 fp.; nd one with 27 ksi (186 MP) low-relxtion strnd initilly tensioned to.7s f. This vrition enbled not only comprison of the lod crrying cpcity of members mde with ech type of strnd, but lso how much of the difference in cpbility is ttributble to the relxtion chrcteristics, nd how much is cused by the difference in initil tension. The significnt results of these computer outputs re summrized in Tbles 1 through 5 nd shown grphiclly in Figs. 1 through 5. Not ll strnd ptterns investigted re shown only those which indicte difference in lod cpcity, which re the mximum number of strnds recommended for ech section. In generl, designs which cll for fewer strnds thn those shown will usully be controlled by the ultimte strength with no increse in cpcity under the ssumptions used. A few generliztions cn be mde s follows: 1. Hollow-core slbs The use of low-relxtion strnd shows n increse in lod cpcity of generlly less thn 1 percent, ll of which is due to less strnd relxtion. Incresing initil tension does not increse cpcity. For mny probbly most pplictions, the mximum spn is limited by ded lod deflection (loss of cmper) in. Double tees This is the most commonly used stemmed section, nd significnt strnd svings cn be relized in mny pplictions by using low-relxtion strnd. For exmple, t spn of 7 ft (21.3 m), with superimposed lod of 4 psf (1.9 kp) [1 psf (.5 kp) ded lod, 3 psf (1.4 kp) live lod], 14 ordinry stress-relieved strnd would be required, wheres 12 lowrelxtion strnds would be dequte, even without incresing the initil tension. Also with the fewer strnd, lower relese strength is required [less thn 35 psi (24 MP) vs. 41 psi (28.3 MP )]. Similr svings re shown in double tees with topping or thickened flnges in the spn rnges most commonly used in prking structures. 3. Long spn roof members For long spn members typified by the 32 in. (813 mm) double tee nd 36 in. (914 mm) single tees investigted, the incresed cpcity becomes even more significnt, s more prestress is required. 4. Bems The investigtion of the 36 in. (914 mm) deep inverted tee bem indicted typicl strnd svings of 18 to 25 percent for these members with the use of low-relxtion strnds. 5. AASHTO girders The AASHTO girder sections were investigted ssuming spcing of 6 ft 6 in. (2. m), with 6'/2 in. (165 mm) thick composite slb. A few other girder spcings were lso checked. In order to mke comprisons, the moment requirements for Stndrd HS2-44 loding for the spns shown, including impct nd lod distribution, were converted to n equivlent required lod per foot. A summry of the computer study is shown in Tble 5 nd Fig. 5. The results indicte tht strnd svings of bout 2 percent would be typicl in the spn rnges indicted. Bsed on losses clculted by Reference 4, when clculted by the method given in the AASHTO Specifictions, $ svings re somewht less. An even greter overll svings is possible on some multi-lne bridges by incresing the spcing enough to reduce the totl number of girders required. Cmber Comprisons Cmber in prestressed concrete members is cused by the prestressing force being pplied eccentriclly with respect to the center of grvity of the member. This is offset by the ded lod 88

6 Tble 1. Uniform lod cpcity (psf) for hollow-core slbs. o v C O u. y F- 8 U h v Spn, $ Z o ci F f^ n o 5 SR LR SR LR SR LR SR LR SR U LR SR LR SR LR SR h 4 LR N SR LR Note: 1 psf =.5 kp; 1 ft =.35 m; 1 in. = 25.4 mm. PCI JOURNAUJuly-August

7 9C LL 81 st 4HC 8 J p 7( U - U M 61 U 51 U- ' 9 s^ \s \^9 LOW-RELAXATION STRAND STRESS- RELIEVED STRAND b 9 9C U. - 8C O J 7( w - c6c W W U-- 4HC12 ^2 ^9 2 \ N U- 8C J W 7( - W D 61 u 5 \ 2 4HC 12 t ou 4 4 Fig. 1. Lod cpcity comprison (hollow-core slbs)

8 Tble 2. Uniform lod cpcity (psf) for 24-in. (61 mm) deep double tees. o o 111 c y Spn, ft Z o i F = 2 N tz 1 SR LR SR LR SR LR SR LR F~ 1 SR C LR c C 12 SR x LR SR LR SR d LR E~ Gl SR LR Note 1 psf =.5 kp, 1 ft =.35 m; 1 in. = 25.4 mm PCI JOURNAL/July-August

9 BC LL U, 7( O J O 6( w - w D 5( w LL 4( U, \ \\\ 8DT 24 9 \ 6 U- U, 7C J O 6C w x 5C U Z) w Ii- 4C U, \\\\ A ^s^ ^9 2 i\ S 8LDT24 '92 OS \ \ bo b3 /V C U. 7( O J O 6( 8DT24+2 \\\_ \N \ \ w U, - w 5( S ^ v2 2 O O \ O LOW-RELAXATION STRAND STRESS-RELIEVED STRAND LL 4( S U, Fig. 2. Lod cpcity comprison [24-in. (61 mm) double tees]. 92

10 Tble 3. Uniform lod cpcity (psf) for long spn members. ^ o v^ Z y ^ S pn, ft c F `n x o N 18 SR LR cv 2 SR E LR C SR LR SR LR SR cd F cn LR oo SR LR SR LR SR n LR SR Note: 1 psf =.5 kp; 1 ft =.35 m. LR PCI JOURNAUJuly-August

11 cd LL ec \ \ ^^ 8DT 32 LL 8 \\ \\\\ 8ST36 U- so \\ \ 8LST 3I 7( Jp 6( U 2 x 5C U n N 4(.9 \\\ \ y s st 9yos 7 J O 6( - 2 5C W W (L 4 ^s^ 9yo\ s stpy y 7 J W 6C - 2 M 5C U N W u 4C '\N ^.y \ vy s N 'An LOW-RELAXATION STRAND STRESS- RELIEVED STRAND --- Fig. 3. Lod cpcity comprison (long spn members)

12 C-) C- C 33 z C- C D C cc c co w Tble 4. Uniform lod cpcity /nlfl for inverted tee hm w i_ ^o. CC -C Z o ci F C F ^^ ^ Spn, ft '" SR LR J 1 8 C 6 J W 241T3 \ \O S \ l ^qti s 14 SR M LR 7 91: J m 4 3 O J TR^^ 16 SR LR SR LR SR LR LOW-RELAXATION STRAND STRESS-RELIEVED STRAND Fig. 4. Cpcity of Type IV AASHTO girder compred with highwy lod requirement. Cn Note: 1 psf =.5 kp; 1 ft =.35 m.

13 13 L J - J L, Z I- z U J \\ \\ \\ \\ \ O W A N \ y S O.g \\3 N ^ A D d W Fig. 5. Cpcity of Type IV AASHTO girder compred with highwy lod requirement. deflection of the member. Creep of the concrete cuses ech of these components to increse with ge, but becuse of losses, the prestress force is being constntly reduced, so the downwrd (deflection) component increses fster thn the upwrd (cmber) component. With low-relxtion strnds, there is less difference in the rte of increse. With proper plnt qulity control over such items s concrete relese strength, strnd plcement (especilly when strnds re depressed t midspn) nd initil tension, the cmber t the time of relese cn be predicted with resonble ccurcy. There re mny more nd less esily controlled fctors which influence long-time cmber, however, nd predictions of wht the cmber will be t criticl times, such s t the time of erection, re t best pproximtions. The computer progrm LODTAB uses the equtions suggested by Mrtin9 for predicting the chnge in cmber over time. His pper is lso the bsis for cmber predictions used in the PCI Design Hndbook. In generl, most precst, prestressed deck members used t their optimum spn nd prestress level will show cmber increse for the first few months, nd then grdul decrese for the reminder of their life. This decrese levels off fter yer or so nd then there is usully no discernble chnge. For roof members on "flt" roofs it is, of course, desirble to hve some upwrd cmber remining in the member so tht ponding is prevented. Thus, it is common nd desirble prctice to limit the spn to lengths tht indicte no worse thn level t the "finl" condition. When low-relxtion strnd is used, this will permit somewht longer spns for deck members before this limiting criterion is reched. Increse of initil tension further increses the spn rnge. Tbles 1 through 5 show these suggested limits, 96

14 Tble 5. Uniform lod cpcity (plf) for AASHTO girders 6 ft 6 in. (2. m) spcing-6'/2 in. (165 mm) thick composite deck. c d - z c v^ - Spn, ft SR LR SR LR SR LR SR LR SR LR SR LR SR LR Note: 1 psf =.5 kp; 1 ft =.35 m bsed on the ssumptions described erlier. It should be noted tht it cn be very dngerous to depend on cmber for roof dringe. A positive slope of t lest 1:1 (nd preferbly more) should be provided in designing ny roof system. For given number of strnds nd prestress level, it is pprent tht the use of low-relxtion strnd will result in more cmber. However, the previous section showed tht for the sme lod cpcity, in mny cses fewer strnds re required, even without n increse PCI JOURNAUJuly-August

15 in initil tension. Doing this will result in less cmber of the members, nd the predictions re likely to be more ccurte. Relese Strength Strnd tensioned to 75 percent of ultimte will obviously require the concrete t time of trnsfer to be of higher strength thn the sme number of strnd tensioned to 7 percent of ultimte, under the criteri imposed by codes nd specifictions. However, s with cmbers, equivlent lod cpcity requires fewer strnds, often without requiring incresed initil tension, so relese strength requirements re less, resulting in further svings. In bems with stright strnds, it is common prctice to reinforce for end tension t relese. With fewer strnds for equivlent cpcity, less reinforcement is required. Effect of Mixing Low-Relxtion Strnd With Ordinry Strnd If the decision is mde to use lowrelxtion strnd, nd if the plnt is mnufcturing products designed for low-relxtion steel, it is highly recommended tht the prestressing plnt convert to it for ll products. This would void the possibility of indvertent use of ordinry strnd in member designed for low-relxtion strnd. However, when using more thn one strnd supplier, occsions my rise when the two types of strnds would be mixed in member. Some specifiers hve expressed concern tht the different properties would hve some detrimentl effects with regrd to possible lterl deflection, cmbers or torsion even if they were designed for ordinry stressrelieved strnd. The clcultions in the Appendix show tht ny such effects re negligible. The member used in the exmple represents the most extreme cse tht could be found mong stndrd products. In fct, the effects shown re probbly even more severe thn would ctully occur, since the difference in prestressing force occurs over time nd creep would tend to neutrlize the differences. Optimizing Strnd Usge In double tees, dditionl strnd svings could be relized by "unblncing" the strnd ptterns. If only even numbers of strnds re used, sttisticlly 5 percent of the members would hve one more strnd thn required. Producers hve been reluctnt to use odd numbers of strnds, such s six in one stem nd seven in the other, becuse of the sme potentil effects illustrted in the clcultions of the previous section. In the cse of unblnced strnd, the mximum force difference, P, would be t the end t relese. If 1/2 in. dimeter, 27 ksi (13 mm, 186 MP) strnd were tensioned to 75 percent of ultimte, this difference (neglecting losses which occur before relese) would be: P = (.153) (27) (.75) = 31 kips (138 kn) using modulus of elsticity t relese of 33 ksi (2.3 x 1 3 MP), corresponding to relese strength of pproximtely 3 psi (21 MP), the mximum lterl sweep (LS) would be (see Appendix): LS =.5 (31./16.8) (215/33) =.6 in. (1.5 mm) The torsionl stress (TS) would be: TS = 5.6 (31./16.8) = 1.3 psi (71 kp) nd the flnge tension (FT): FT = 92 (31./16.8) = 17 psi (117 kp) 98

16 This is less thn the crcking stress, even when the compression cused by grvity lods is not included. CONCLUSIONS The nlyses mde in this pper indicte tht the use of low-relxtion strnd cn result in significnt strnd svings for virtully ll types of precst, prestressed stndrd products for designs pproching mximum cpbility. This is especilly true in longer, hevier structurl members. For exmple, the svings will be less with hollow-core slbs thn with bridge girders. Low-relxtion strnd cn lso provide improvements in deflection nd crcking control. It ws lso shown tht low-relxtion strnd cn be mixed with stress-relieved strnd in design bsed on stress-relieved strnd properties without hrmful effects. With the much improved properties of low-relxtion strnd over stress-relieved strnd, nd with the price of it being competitive with stress-relieved, low-relxtion strnd will undoubtedly become the stndrd of the industry. ACKNOWLEDGMENT This pper is bsed upon study conducted by The Consulting Engineers Group of Glenview, Illinois, under contrct with Armco, Union Wire Rope, Knss City, Missouri. REFERENCES 1. ASTM Stndrd A416-8 "Specifiction for Uncoted Seven-Wire Stress-Relieved Strnd for Prestressed Concrete," Americn Society for Testing nd Mterils, Phildelphi, Pennsylvni, ASTM Stndrd E328-78, "Recommended Prctice for Stress-Relxtion Tests for Mterils nd Structures," Americn Society for Testing nd Mterils, Phildelphi, Pennsylvni, PCI Design Hndbook -Precst nd Prestressed Concrete, Second Edition, 1978, Prestressed Concrete Institute, Chicgo. 4. Zi, Pul, Preston, H. K., Scott, N. L., nd Workmn, E. B., "Estimting Prestress Losses," Concrete Interntionl, V. 1, No. 6, June 1979, pp ACI-ASCE Committee 423 (formerly 323), "Tenttive Recommendtions for Prestressed Concrete," ACI Journl, Proceedings V. 54, No. 7, Jnury 1958, pp ACI Committee 318, "Building Code Requirements for Reinforced Concrete (ACI )," (including Commentry), Americn Concrete Institute, Detroit, Michign, PCI Committee on Prestress Losses, "Recommendtions for Estimting Prestress Losses," PCI JOURNAL, V. 2, No. 4, July-August 1975, pp Stndrd Specifictions for Highwy Bridges, Twelfth Edition, Americn Assocition of Stte Highwy nd Trnsporttion Officils, Wshington, D.C., Mrtin, L. D., "A Rtionl Method for Estimting Cmber nd Deflection of Precst Prestressed Concrete Members," PCI JOURNAL, V. 22, No. 1, Jnury- Februry 1977, pp Note: A design exmple is provided in the Appendix on the following two pges. PCI JOURNAL/July-August

17 APPENDIX - DESIGN EXAMPLE This design exmple shows the effect of mixing low-relxtion strnd nd stress-relieved strnd. The effect would be gretest in double-tee member where the mximum number of strnds were spced the mximum lterl distnce prt. From the PCI Design Hndbook, select 1DT32 section with 22 ' -in. (12.7 mm) dimeter, 27 ksi (186 MP) strnds. IO'-"(3.5m) 3 5'-"(1.5 m) II STRESS-RELIEVED STRANDS It LOW RELAXATION STRANDS The section properties nd strnd detils re s follows: I,z = 626,791 in. 4 (1.3 x 1 1 mm4) I, = 59,72 in. 4 (9.79 x 18 mm4) Strnd eccentricity: e e = 5.57 in. (141 mm) e, = in. (444 mm) e = in. (33 mm) Stress to 7 percent ultimte:.7x27= 189 ksi (133 MP) Strnd re per stem: 11 x.153 = in. 2 (19 mm2) Assume mximum prestress loss (ccording to the recommendtions in Reference 6). Finl strnd stress: Low-relxtion strnd = = 149 ksi Stress-relieved strnd = = 139 ksi = 1 ksi (69 MP) The difference in the finl prestress force is: P = 1 x 1.68 = 16.8 kips (74.7 kn) Assume tht: f,' = 5 psi (34.5 MP) E, = 43 ksi (3. x 14 MP) To ccount for creep, use the longterm vlue: 4t = 2` = 215 ksi (1.5 x 1 4 MP) Spn = 86 ft (26.2 m) 1. Potentil lterl deflection (sweep): Pel 2 _ 16.8 (3) (86 x 12)2 8E1 8 (215) (626,791) =.5 in. (1.3 mm) which is negligible quntity. 2. Potentil torsionl stresses: The theoreticl difference in upwrd cmber of ech stem is: 1

18 in which Pe e l 2Pe'l2 8E1 + 12E1 z P ee+ e ndl= EI Therefore: _ 16.8 (86 x 12) ,15 x 29,86 [ =.471 in. (12 mm) The equivlent uniform lod to cuse the sme deflection is found from the eqution: from which the weight W= 24.6x86 = 2,113 lb (9,345 N) The torsionl moment equls: T = 2,113 x 3 = 63,39 in.-lb The polr moment of inerti is found from the sum: J =Ix+Iv = 626, ,72 = 686,511 in.4 The distnce from the neutrl xis is: = 5w1' 384E1 c = b/2 = 6 in. (1524 mm) or The torsionl stress is obtined from: _ 384EI A W 514 Tc 63,39 x 6 _ 384 (2,15) (29,86) (.471) J (86 x 12) = 5.6 psi (38.6 kp) = 24.6 lb per ft (359 N/m) which is obviously negligible. t R 24.6 LB/ FT. 3^^ 3. Potentil flnge stress With reference to the sketch: M = 24.6 (3) = 738 in.-lb per ft Section modulus of flnge: bd 2 12 (2) 2 = 8 in. 3 per ft 6 6 Mximum tensile stress: S 8 = 92 psi (634 kp) The computed tensile stress is much less thn tht which would cuse crcking even neglecting compression from grvity lods. NOTE: Discussion of this pper is invited. Plese submit your comments to PCI Hedqurters by Mrch 1, PCI JOURNAL/July-August